On groups with chordal power graph, including a classification in the case of finite simple groups [PDF]
Journal of Algebraic Combinatorics, 2023 AbstractWe prove various properties on the structure of groups whose power graph is chordal. Nilpotent groups with this property have been classified by (Electron J Combin 28(3):14, 2021). Here we classify the finite simple groups with chordal power graph, relative to typical number theoretic conditions.
Jendrik Brachter, Eda Kaja
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The classification of finite simple groups I. Simple groups and local analysis [PDF]
Bulletin of the American Mathematical Society, 1979 It is indeed unfortunate that Richard Brauer did not live to see the complete classification of the finite simple groups. He had devoted the past thirty years largely to their study and it is difficult to overestimate the impact he made on the subject ...
D. Gorenstein
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Maximal subgroups of finite simple groups: classifications and applications [PDF]
BCC, 2021 This paper surveys what is currently known about the maximal subgroups of the finite simple groups. After briefly introducing the groups themselves, if their maximal subgroups are completely determined then we present this classification. For the remaining finite simple groups our current knowledge is only partial: we describe the state of play, as ...
C. Roney-Dougal
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Towards the classification of finite simple groups with exactly three or four supercharacter theories [PDF]
Asian-European Journal of Mathematics, 2018 A supercharacter theory for a finite group [Formula: see text] is a set of superclasses each of which is a union of conjugacy classes together with a set of sums of irreducible characters called supercharacters that together satisfy certain compatibility conditions.
Fatemeh Koorepazan-Moftakhar +1 more
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On the classification of finite simple groups by the number of involutions [PDF]
Proceedings of the American Mathematical Society, 1979 Simple groups with k involutions, where k ≡ 1 k \equiv 1 (modulo 4), are completely determined.
M. Herzog
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Group Knowledge and Mathematical Collaboration: A Philosophical Examination of the Classification of Finite Simple Groups [PDF]
Episteme, 2021 AbstractIn this paper we apply social epistemology to mathematical proofs and their role in mathematical knowledge. The most famous modern collaborative mathematical proof effort is the Classification of Finite Simple Groups. The history and sociology of this proof have been well-documented by Alma Steingart (2012), who highlights a number of ...
Joshua Habgood-Coote +1 more
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A brief history of the classification of the finite simple groups [PDF]
Bulletin of the American Mathematical Society, 2001 We present some highlights of the 110-year project to classify the finite simple groups.
R. Solomon
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The Classification of Finite Simple Groups: A Progress Report
Notices of the American Mathematical Society, 2018 This is an expository note focused upon one example, the irrational rotation C∗-algebra. We discuss how this algebra arises in nature—in quantum mechanics, group actions, and foliated spaces, and we explain how K-theory is used to get information out of ...
R. Solomon
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Afterword to the article “A brief history of the classification of the finite simple groups” [PDF]
Bulletin of the American Mathematical Society, 2018 In this afterword the author discusses his previously published article “A brief history of the classification of the finite simple groups”, which appeared in Bull. Amer. Math. Soc. (N.S) 38 (2001), no. 3, 315–352.
R. Solomon
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An introduction to the classification of finite simple groups [PDF]
Bulletin of the American Mathematical Society, 1979 The classification of the finite simple groups now seems close at hand. You may judge for yourself just how close from Daniel Gorenstein's article in this Bulletin, introduced below.
M. Aschbacher
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